Error Estimates For The Hp-version Of The DG Method Based On Upwind-biased Fluxes

In this paper, we present an analysis of the Runge-Kutta discontinuous Galerkin method based on upwind-biased fluxes for solving one-dimensional variable coefficient hyperbolic laws. We provide the L2 stability analysis and the hp error estimates both for the semidiscrete and fully discrete scheme. The upwind-biased fluxes are depending withθj+1/2 at every nodes(j= 1,2,…, N). In semidiscrete scheme, we prove that the hp error is relating with the θj+1/2, and when the θj+1/2 are same, the error has the monotonicity with the 9. In fully discrete scheme, we discuss the TVDRK2 and TVDRK3 methods when using the CFL condition of the time step τ, the element length h and the degree of the piecewise polynomials p. Numerical experiments are shown to demonstrate the theoretical results with different θ, h and p.